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Q.

If the slope of a straight line passing through A(3,2) is 3/4, then the coordinates of the two points on the same line that are 5 units away from A are

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a

$(6, 3), (- 2, - 3)$

b

$(- 7, 5), (1, - 1)$

c

$(6, 9), (- 2, 3)$

d

$(7, 5), (- 1, - 1)$

answer is B.

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Detailed Solution

$\begin{aligned} (x_{1}, y_{1}) = (3, 2) \\ \tan θ = \frac{3}{4} \sin θ = \frac{3}{5}, \cos θ = \frac{4}{5} \\ (x, y) = (x_{1} \pm r \cos θ, y_{1} \pm r \sin θ) = \\ (3 \pm 5 (\frac{4}{5}), 2 \pm 5 (\frac{3}{5})) = (3 \pm 4, 2 \pm 3) \\ = (7, 5) (- 1, - 1) \end{aligned}$

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